What is this Lord of the Rings song called?

I'm looking for the name and (if possible) youtube link to this Lord
of the Rings song:

http://www.youtube.com/watch?v=QRsVaeDhZ…

(I recorded this off my phone from the game LOTR: Battle for Middle
Earth 2. I want a better quality, full version. Obviously)

It sounds very similar to Into The West, but without the singing, and
the flute I believe. It is a version I have not been able to find
anywhere (if it is a version at all).

Any help would be great.